Health economic evaluations of interventions against infectious diseases are commonly based on the predictions of compartmental models such as ordinary differential equation (ODE) systems and Markov models. In contrast to standard Markov models which are static, ODE systems are dynamic by definition and therefore able to account for the effects of herd immunity. This is crucial in pathogens which are transmissible between humans to prevent incorrect model outcomes. The computational effort of fully probabilistic ODE systems is considerably high. Thus, most ODE-based models in the literature are deterministic; they do not account for parameter uncertainty and probabilistic sensitivity analysis cannot be conducted straightforwardly. Yet, it is an essential part of health economic evaluations to investigate the impact of parameter uncertainty on decision making. We present an innovative approach of a dynamic Markov model with Bayesian inference. We extend a static Markov model by directly incorporating the force of infection of the pathogen into the health state allocation algorithm, accounting for the effects of herd immunity. As a consequence, the output of our fully probabilistic Bayesian Markov model is based on dynamic interactions between individuals, and at the same time eligible to conduct probabilistic sensitivity analysis straightforwardly. We introduce a case study of a fictional chronic sexually transmitted infection. By means of this constructed example, we show that our methodology produces results which are comparable to a Bayesian ODE system, yet at lower cost of implementation and computation. In contrast to probabilistic methodology, deterministic models tend to underestimate disease prevalence and thus the benefits of vaccination.